Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8031,2,Mod(1,8031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8031, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8031 = 3 \cdot 2677 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8031.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1278578633\) |
Analytic rank: | \(1\) |
Dimension: | \(102\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
$q$-expansion
The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.
Embeddings
For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.
For more information on an embedded modular form you can click on its label.
comment: embeddings in the coefficient field
gp: mfembed(f)
Label | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1.1 | −2.77663 | −1.00000 | 5.70967 | 2.19491 | 2.77663 | −1.70746 | −10.3004 | 1.00000 | −6.09446 | ||||||||||||||||||
1.2 | −2.71515 | −1.00000 | 5.37202 | 0.694821 | 2.71515 | 4.70425 | −9.15552 | 1.00000 | −1.88654 | ||||||||||||||||||
1.3 | −2.70545 | −1.00000 | 5.31943 | −1.42429 | 2.70545 | −0.675914 | −8.98054 | 1.00000 | 3.85333 | ||||||||||||||||||
1.4 | −2.68439 | −1.00000 | 5.20592 | −2.39911 | 2.68439 | 1.70434 | −8.60593 | 1.00000 | 6.44014 | ||||||||||||||||||
1.5 | −2.65332 | −1.00000 | 5.04013 | 4.03395 | 2.65332 | 0.348072 | −8.06646 | 1.00000 | −10.7034 | ||||||||||||||||||
1.6 | −2.63837 | −1.00000 | 4.96099 | −0.827443 | 2.63837 | 4.06107 | −7.81219 | 1.00000 | 2.18310 | ||||||||||||||||||
1.7 | −2.63608 | −1.00000 | 4.94890 | −1.93801 | 2.63608 | 2.42840 | −7.77354 | 1.00000 | 5.10875 | ||||||||||||||||||
1.8 | −2.50066 | −1.00000 | 4.25331 | −3.45059 | 2.50066 | −2.37826 | −5.63477 | 1.00000 | 8.62875 | ||||||||||||||||||
1.9 | −2.41582 | −1.00000 | 3.83616 | −4.10960 | 2.41582 | 3.79885 | −4.43583 | 1.00000 | 9.92804 | ||||||||||||||||||
1.10 | −2.40685 | −1.00000 | 3.79292 | −3.26734 | 2.40685 | −0.892865 | −4.31530 | 1.00000 | 7.86399 | ||||||||||||||||||
1.11 | −2.38361 | −1.00000 | 3.68158 | 1.26527 | 2.38361 | −2.62916 | −4.00822 | 1.00000 | −3.01590 | ||||||||||||||||||
1.12 | −2.34132 | −1.00000 | 3.48177 | 2.61787 | 2.34132 | 0.261983 | −3.46929 | 1.00000 | −6.12927 | ||||||||||||||||||
1.13 | −2.32872 | −1.00000 | 3.42294 | 3.08451 | 2.32872 | −2.29057 | −3.31363 | 1.00000 | −7.18297 | ||||||||||||||||||
1.14 | −2.29383 | −1.00000 | 3.26167 | 1.63510 | 2.29383 | 1.45930 | −2.89406 | 1.00000 | −3.75066 | ||||||||||||||||||
1.15 | −2.17521 | −1.00000 | 2.73153 | −1.76548 | 2.17521 | 3.60234 | −1.59123 | 1.00000 | 3.84028 | ||||||||||||||||||
1.16 | −2.09321 | −1.00000 | 2.38154 | −1.37232 | 2.09321 | −2.95047 | −0.798646 | 1.00000 | 2.87257 | ||||||||||||||||||
1.17 | −2.08872 | −1.00000 | 2.36276 | 1.75391 | 2.08872 | 4.99893 | −0.757708 | 1.00000 | −3.66343 | ||||||||||||||||||
1.18 | −2.02856 | −1.00000 | 2.11504 | −0.0759576 | 2.02856 | −4.07042 | −0.233369 | 1.00000 | 0.154084 | ||||||||||||||||||
1.19 | −2.01958 | −1.00000 | 2.07869 | −3.91431 | 2.01958 | 1.55136 | −0.158921 | 1.00000 | 7.90525 | ||||||||||||||||||
1.20 | −1.93543 | −1.00000 | 1.74588 | −1.47227 | 1.93543 | 2.60220 | 0.491826 | 1.00000 | 2.84947 | ||||||||||||||||||
See next 80 embeddings (of 102 total) |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(3\) | \(1\) |
\(2677\) | \(1\) |
Inner twists
This newform does not admit any (nontrivial) inner twists.
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 8031.2.a.b | ✓ | 102 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
8031.2.a.b | ✓ | 102 | 1.a | even | 1 | 1 | trivial |